Wireless devices such as cell phones, tablets, and laptops require integrated circuits that operate at radio frequencies (RFICs). Embedded inductor coils are used in RFICs such as voltage controlled oscillators, low noise amplifiers, power amplifiers, mixers, filters and matching networks. Embedded transformers are used for power converters, to pass signals from a first integrated circuit or sub-circuit that operates at one voltage to a second integrated circuit or sub-circuit that operates at a different voltage, and to electrically isolate two integrated circuits that operate at the same voltage.
On-chip embedded inductors and transformers in commercially available planar semiconductor processes exhibit a low quality factor (Q), due to energy losses. The energy losses occur as the result of the coupling between the inductor coils and transformer coils and the underlying low resistance silicon substrate. Q is given by Equation 1:
                    Q        =                  2          ⁢          π          ⁢                                                    peak                ⁢                                                                  ⁢                magnetic                ⁢                                                                  ⁢                energy                            -                              peak                ⁢                                                                  ⁢                electronic                ⁢                                                                  ⁢                energy                                                    energy              ⁢                                                          ⁢              dissipated              ⁢                                                          ⁢              per              ⁢                                                          ⁢              cycle              ⁢                                                          ⁢              of              ⁢                                                          ⁢              oscillation                                                          (        1        )            
When current flows through the windings of an embedded inductor coil or an embedded transformer coil, the magnetic fields induced around the coil extend into the underlying semiconductor substrate to a depth that is proportional to size of the embedded inductor or transformer coil. The silicon substrate is conductive and the time varying magnetic field induces an electric field (E) in the substrate. The electric field induces a parasitic eddy current in the substrate. The parasitic eddy current flows in a direction opposing the current flowing in the embedded inductor coil or transformer coil. The parasitic eddy current acts similar to a current due to a shorted secondary winding in a parasitic transformer and can reduce the Q for the coil by 50% or more. The reduction in Q results in reduced power transfer efficiency and limits the frequency of operation.